How to COMPUTE Eigenvalues and Eigenvectors | FREE Linear Algebra Course

In this video, we learn how to compute eigenvalues and eigenvectors of a matrix. We compute the eigenvalues as roots of the characteristic polynomial. We compute eigenvectors as non-zero vectors of the eigenspace. We also define and compute algebraic multiplicity and geometric multiplicity of eigenvalues.

This video is part of a linear algebra course

Students often ask is linear algebra important and is linear algebra hard. They wonder can anyone learn linear algebra and why some can't understand linear algebra. It is important to show to the students how linear algebra is used in data science, machine learning, AI, computer science, image processing, computer graphics, and in real life in general. This is a free video course in linear algebra for everyone, even beginners. It covers linear algebra with applications.

CHAPTERS:
0:00 Intro and learning outcomes
0:32 How to compute eigenvalues
3:00 Characteristic polynomial
3:20 Eigenvalues are roots of the characteristic polynomial
3:33 Example: computing eigenvalues
4:41 Eigenspace
6:54 Eigenspace is a subspace
10:44 Example: computing eigenvectors
12:16 Strategy for computing eigenvalues and eigenvectors
12:49 Algebraic and geometric multiplicity of eigenvalues
13:56 Example: algebraic and geometric multiplicities
15:07 Now what?

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